# Distance between 2 atoms in a crystal

## Homework Statement

Given a crystal (cube) with regularly arranged atoms (Total 27 atoms)
The mass of each atom is 3.5*10^-25. The density of the crystal is 9.2*10^3
What is the shortest distance between the centres of two adjacent atoms?

## Homework Equations

density = mass / volume

## The Attempt at a Solution

Volume= (27*3.5*10^-25)/(9.2*10^3)=1.03*10^-27
Length(L)=1*10-9
Distance between two atoms is L/2=5.04*10^-10

do you thinkthis is the correct answer?

L is correct. Should you really be dividing by 2?

Sorry the correct answer should be 3.4*10^-10
Should I divide by 3 then ? Why ?

What you probably did was to assume the volume of 27 atoms had an atom at every corner and one between. But if you put this volume next to another, the atoms on the edges would be to close. In fact, the distance should be 3.

But if you put this volume next to another, the atoms on the edges would be to close.
So the atoms on the edges would be closer than others and that's the required "shortest distance"?
I just can't really imagine what it looks like

Maybe I wasn't clear. Put the atoms in a uniform rectangular three dimensional grid. My attachment shows the top view. Notice the volume is (3d)^3

#### Attachments

• x120.jpg
36.7 KB · Views: 873
haruspex